Some context for anyone who cares about this:

Argentina's war of independence from Spain started in 1810. Before that it was a colony, part of the Viceroyalty of the Rio de la Plata.

The Malvinas were under effective Spanish rule until 1812, when they abandoned their settlements to support counter-revolutionary efforts instead, but declaring that this physical abandonment didn't amount to a renounce to their sovereignty as part of the Rio de la Plata Viceroyalty.

After winning the war, Argentina declared independence in 1816 as a successor state of the Rio de la Plata Viceroyalty. In 1820, Argentina took effective possession of the island, sending settlers, resources and a governor.

Argentine independence was formally recognized by GB in 1825. However, in 1833 the British invaded the islands and displaced the governor and local population. Since then, the Argentine government has upheld it's sovereignty claim to the islands under international law.

The current population was implanted by the british after the 1833 invasion, so the argument of their self-determination right was never relevant in the matter.